Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.) 1 lim X→-8+ X + 8

Q: (26) Denote the second Fourier sine coefficient on the interval [-L, L] by L A2 = / f(x) sin -L Show…

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Q: Cos 4x S cos 2x-sin 2x dx

A: This is a problem related to integration. Based on the general formula and concepts we will answer…

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A: This is a problem related to derivative of the triangle. Based on the general formula and concept we…

Q: Test the series for convergence or divergence. E(-1yr (3n – 1). 7n +1 n-1 Evaluate the following…

A: Recall: Divergent theorem,    If limn→∞an≠0, then the given series ∑n=1∞an is divergent. We have,…

Q: 15. The solution of Laplace equation и + 3 0, и(х,0) — 0, и(х, п) — 0, и (о, у) — 0, и(0, у) %— 3sin…

A: Please see the below picture for detailed solution.

Q: Sketch the graph of an example of a function f that satisfies all of the given conditions. f(x) = 4,…

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Q: f(0) =| f'(0) f"(0) T | ||

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Q: The solution of the differential equation below is dy 3y + 4x = 0 %3D dx *

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Q: obtain the values of y at x = 0.1, 0.2 using R.K method of fourth order Por the differential…

A: Let's find.

Q: An open box is to be made by cutting small squares from the corners of rectangular board and then…

A: let "x" be the length of the side of the square cut.Length= 8-2xWidth = 6-2xHeight =xVolume =…

Q: Find f, and f, as functions if 2y f(x. y) = y+ y + cos x

A: This question is related to differentiation, We will solve it using given information.

Q: This matrix is a 0 0 4 0 [ 4 0 0 zero matrix square matrix diagional matrix unit matrix O

A: Given problem:-

Q: Find the inverse of the function. f (x) = 14 – 5x³

A: Topic = Function

Q: Determine the equation of the tangent plane to the surface z = cos(x + 2y) at the point (2,-1,0).

A: Tangent plane to f(x, y) at (x0, y0) is given by below:

Q: Calculate the upper sums Un and lower sums Ln, on a regular partition of the intervals, for the…

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Q: 6. For each function determine: i) the critical values ii) the intervals of increasing or decreasing…

A: Given problem:- f(x) = x3 - 9x2 + 24x - 10 To find:- i) the critical values   ii) the intervals of…

Q: Express the integral as a limit of right endpoint Riemann sums. Do not evaluate the limit. 8 + x2 dx

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Q: A factory selling cell phones has a marginal cost function C(x) = 0.01? -3x + 229, where z…

A: Given problem:- A factory selling cell phones has a marginal cost function C(x) = 0.01x2 - 3x + 229…

Q: Dwing equations Is an exact different: v = 0 2xydx + (2 + an 1 O

A: We have to choose the correct option from the given options according to the given information

Q: 4. Find 2+1dt O V4x+1 O V16x? +1+v2 O 4/16x? +1 O V16x? +1

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Q: Determine which inverse trigonometric function g has the derivative g'(x) (Use symbolic notation and…

A: Given g'(x)=1x2+1 Integrating on both sides, we have ∫g'(x) dx=∫1x2+1 dx

Q: Calculate the surface integral / G(r) dA, where G = (12xz + 36)1/2, the surface S is given by the…

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Q: This problem has two parts. The second part will appear after you answer the first part correctly.…

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Q: Evaluate with out hoH LnX lim

A: The given limit is: limx→1lnxx-1   As we know from the Taylor series with center 1:…

Q: y" + 3y + 2y = x2

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Q: 9. S sec³ x tan x dx

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Q: Let f : R → R be an odd differentiable function. Define F: R2 → R by F(x, y) = f(x² + xy+9y²). (a)…

A: This is a problem of differentiating function. Based on the concept of partial differentiation we…

Q: 11. ſ sin? x cos² x dx

A: Given ∫sin2x cos2x dxTo find integration:

Q: The current population of a certain bacteria is 5410 organisms. It is believed that bacteria's…

A: Given, Initial population (P)=5410 , Rate of multiples (R)=3 , Triplet in 9 minutes. Therefore n=9…

Q: -5t i + j+ sin(3t) k sin (t) lim e t 0

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Q: 1

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Q: OGraph the following Runetion two -4

A: Graph

Q: There is a function                                                           f(x,y)=3√x3 + y.…

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Q: Use the formula k(t) : ||r() × r"(t)|| to find K(t). %3D r(t) = t²i + t®j %3D

A: Given that,     r(t)=t2i+t9j

Q: s being pumped into a spherical ballo nge of the radius when the radius reac

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Q: BASIC CALCULUS 1. The line segment from (1, -1,3) to (0, –3, 1) forms a diameter of the sphere S1.…

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Q: This equation is an example for linear equations dy y = = x²e* dx True False O +

A: Any differential equation of nth order is linear if it is of 1st degree and donot have product of…

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A: Take a homogenous equation and first differentiate then simplify

Q: H.W. 1. Find the arc length of the curve x = (y + 2)/2 from y=0 to y=1

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Q: a lim - o Consider the following series. * (-1)* * 1 (jerror 0, and then you need to verify the two…

A: Given: Here, bn+1=(-1)n+1+1n+17=1n+17. We are given the bound ε=0.00005. So, now we need to solve…

Q: Show that fu,, u2, uz) is an orthogonal basis for R. Then express x as a linear combination of the…

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Q: Using appropriate substitution tan3. dx sec5x tan³x is equal to

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Q: B.vL XI らX、 X3 SOL 2. -11 zjjo 7. Find the values of a, b, c and find the sol 1. C. 9.

A: Given

Q: Solution :- we have Fla) =5 cas 2x %3D Now di'fferentiate it wot x x d (cos2x) %3D Źx(-2sin2x) %3D…

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Q: P(x) Let P(x) and Q (x) be polynomials with the degree of Q (x) greater than the degree of P(x) and…

A: Here we have given that P(x) & Q (x) be polynomial such that degree of Q(x) is greater than P(x)…

Q: Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values…

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Q: dx In x +1+ Vx² + 2x| + C Vx2 + 2x

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Q: 2 4-x Find the area in the first quadrant bounded by the coordinate axes and the graph of y = 5 The…

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Q: Given the curve y = x' and the line y = 2 – x. Find the area of the region bounded by the curve and…

A: Area bounded by the curve y=x2 and the line y=2-x

Q: x3 dx J4- x4

A: ∫x3dx4-9x4Multiply & divide by -36 =-136∫-36x3dx4-9x4since, ∫f'(x)f(x)dx= 2f(x)